Properties

Label 87120.bn
Number of curves $6$
Conductor $87120$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 87120.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.bn1 87120t4 \([0, 0, 0, -57499563, -167820468662]\) \(15897679904620804/2475\) \(3273096420633600\) \([2]\) \(3932160\) \(2.8236\)  
87120.bn2 87120t6 \([0, 0, 0, -30492363, 63566853658]\) \(1185450336504002/26043266205\) \(68882522341166464296960\) \([2]\) \(7864320\) \(3.1702\)  
87120.bn3 87120t3 \([0, 0, 0, -4138563, -1774758062]\) \(5927735656804/2401490025\) \(3175882183844361446400\) \([2, 2]\) \(3932160\) \(2.8236\)  
87120.bn4 87120t2 \([0, 0, 0, -3594063, -2621673362]\) \(15529488955216/6125625\) \(2025228410267040000\) \([2, 2]\) \(1966080\) \(2.4771\)  
87120.bn5 87120t1 \([0, 0, 0, -190938, -53675237]\) \(-37256083456/38671875\) \(-799095805818750000\) \([2]\) \(983040\) \(2.1305\) \(\Gamma_0(N)\)-optimal
87120.bn6 87120t5 \([0, 0, 0, 13503237, -12913790582]\) \(102949393183198/86815346805\) \(-229620202734149609564160\) \([2]\) \(7864320\) \(3.1702\)  

Rank

sage: E.rank()
 

The elliptic curves in class 87120.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 87120.bn do not have complex multiplication.

Modular form 87120.2.a.bn

sage: E.q_eigenform(10)
 
\(q - q^{5} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.